The finding in the present work that a non-traditional renormalization scheme is needed to tackle the cosmological constant problem is in line with the observation, e.g., in [1]}. The overarching umbrella for this and [2]}, [3]}, [4]}, [5]}, [6]} is the so-called running vacuum with time-varying and dynamical energy, a view that we find very natural. In these works, the cosmological constant problem was coherently tackled from different angles and various cosmological implications of such a vacuum were discussed. (Even the relevance of temperature to the cosmological constant problem was discussed to some extent.)
Several different regularization methods and their pertinent renormalization schemes were analyzed. We believe that the present work lends support, by providing independent motivation to consider a non-standard renormalization scheme, to those approaches. It is also interesting to note that the present finite temperature contribution to the stress-energy tensor seems to bear a certain resemblance to the `stress-energy tensor of cosmic interaction' obtained in [7]}.
